Combine onion, jalapeno, scallions and parsley in a food processor or blender, and pulse to a rough puree.

Whisk together the cornmeal, flour, sugar, baking powder, salt, thyme and cayenne in a small bowl. In a separate bowl, whisk together the milk and egg. Add the vegetable puree and stir to combine. Add the wet ingredients to the dry ingredients and stir until combined. For best results, refrigerate the batter for at least 30 minutes before frying.

Heat 3 inches of oil in a 4- to 5-quart heavy pot (preferably cast iron) over high heat until it reaches 350 degrees. Carefully add the batter to the hot oil 1 heaping tablespoon at a time, working in batches of six; use another spoon to scrape the batter into the oil, keeping it in a ball shape.

Fry, turning, until golden, 2 to 3 minutes, then transfer with a slotted spoon to paper towels to drain briefly. Transfer the hush puppies to a shallow baking pan and keep hot in a 200-degree oven while frying remaining batter. Heat the oil back to 350 degrees between batches.